Quantum optimal control methods [1]} have been successfully used on a variety of platforms, including superconducting qubits [2]}, [3]}, [4]}, [5]}, trapped ions [6]}, [7]} and neutral atoms [8]}, [9]}, [10]}, [11]}, [12]}.
For neutral atoms,
three properties of the laser pulses implementing a given gate are of particular interest: (i) They should be time-optimal (i.e., as short as possible) because many errors mentioned above can be mitigated by short pulse durations; (ii) They should ideally require only a global control laser addressing all atoms of the gate simultaneously – so-called global pulses –, instead of requiring single-site addressability, in order to simplify experiments; (iii) They should allow for executing three and more qubit gates natively (i.e., without decomoposing them into single- and two-qubit gates).
In line with these three requirements, a remarkable result in Ref. [13]} shows that a global pulse for the Controlled-Z (CZ) gate exists, which is more then 30% faster than the original, non-global proposal [14]}, and a global pulse exists for a Toffoli gate, albeit only with a moderate theoretically predicted fidelity of 97.6%. Naturally the question arises if it is possible to find pulses that are even faster and achieve higher fidelities, in order to make both CZ and C\(_2\) Z gates fully compatible with error correction schemes.
